There are 15 sajdas in Quran, as comes in this Hadith:
Narrated Amr ibn al-'As: The Prophet () taught me fifteen prostrations
while reciting the Qur'an, including three in al-Mufassal and two in
Surah al-Hajj. Abu Dawud said: Abu al-Darda' has reported eleven
prostrations from the Prophet (), but chain of this tradition is weak.
حَدَّثَنَا مُحَمَّدُ بْنُ عَبْدِ الرَّحِيمِ بْنِ الْبَرْقِيِّ،
حَدَّثَنَا ابْنُ أَبِي مَرْيَمَ، أَخْبَرَنَا نَافِعُ بْنُ يَزِيدَ،
عَنِ الْحَارِثِ بْنِ سَعِيدٍ الْعُتَقِيِّ، عَنْ عَبْدِ اللَّهِ بْنِ
مُنَيْنٍ، - مِنْ بَنِي عَبْدِ كُلاَلٍ - عَنْ عَمْرِو بْنِ الْعَاصِ،
أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم أَقْرَأَهُ خَمْسَ عَشْرَةَ
سَجْدَةً فِي الْقُرْآنِ مِنْهَا ثَلاَثٌ فِي الْمُفَصَّلِ وَفِي سُورَةِ
الْحَجِّ سَجْدَتَانِ . قَالَ أَبُو دَاوُدَ رُوِيَ عَنْ أَبِي
الدَّرْدَاءِ عَنِ النَّبِيِّ صلى الله عليه وسلم إِحْدَى عَشْرَةَ
سَجْدَةً وَإِسْنَادُهُ وَاهٍ .
Sunan Abu Dawud
They are in the following Ayat(in order):
Also note that performing the sajdah is not obligatory but is a stressed (confirmed) sunnah (سنة مؤكدة) that is highly recommended to follow. Here is a hadith:
Narrated Rabi'a: 'Umar bin Al-Khattab recited Surat-an-Nahl on a
Friday on the pulpit and when he reached the verse of Sajda he got
down from the pulpit and prostrated and the people also prostrated.
The next Friday 'Umar bin Al-Khattab recited the same Sura and when he
reached the verse of Sajda he said, "O people! When we recite the
verses of Sajda (during the sermon) whoever prostrates does the right
thing, yet it is no sin for the one who does not prostrate." And 'Umar
did not prostrate (that day). Added Ibn `Umar "Allah has not made the
prostration of recitation compulsory but if we wish we can do it."
حَدَّثَنَا إِبْرَاهِيمُ بْنُ مُوسَى، قَالَ أَخْبَرَنَا هِشَامُ بْنُ
يُوسُفَ، أَنَّ ابْنَ جُرَيْجٍ، أَخْبَرَهُمْ قَالَ أَخْبَرَنِي أَبُو
بَكْرِ بْنُ أَبِي مُلَيْكَةَ، عَنْ عُثْمَانَ بْنِ عَبْدِ الرَّحْمَنِ
التَّيْمِيِّ، عَنْ رَبِيعَةَ بْنِ عَبْدِ اللَّهِ بْنِ الْهُدَيْرِ
التَّيْمِيِّ ـ قَالَ أَبُو بَكْرٍ وَكَانَ رَبِيعَةُ مِنْ خِيَارِ
النَّاسِ عَمَّا حَضَرَ رَبِيعَةُ مِنْ عُمَرَ بْنِ الْخَطَّابِ ـ رضى
الله عنه ـ قَرَأَ يَوْمَ الْجُمُعَةِ عَلَى الْمِنْبَرِ بِسُورَةِ
النَّحْلِ حَتَّى إِذَا جَاءَ السَّجْدَةَ نَزَلَ فَسَجَدَ وَسَجَدَ
النَّاسُ، حَتَّى إِذَا كَانَتِ الْجُمُعَةُ الْقَابِلَةُ قَرَأَ بِهَا
حَتَّى إِذَا جَاءَ السَّجْدَةَ قَالَ يَا أَيُّهَا النَّاسُ إِنَّا
نَمُرُّ بِالسُّجُودِ فَمَنْ سَجَدَ فَقَدْ أَصَابَ، وَمَنْ لَمْ
يَسْجُدْ فَلاَ إِثْمَ عَلَيْهِ. وَلَمْ يَسْجُدْ عُمَرُ ـ رضى الله
عنه. وَزَادَ نَافِعٌ عَنِ ابْنِ عُمَرَ ـ رضى الله عنهما إِنَّ
اللَّهَ لَمْ يَفْرِضِ السُّجُودَ إِلاَّ أَنْ نَشَاءَ.
[Sahih Bukhari]
Also here is a hadith about how good performing sajdah is:
It is narrated on the authority of Abu Huraira that when, the son of
Adam recites the Ayat of Sajdah (prostration) and then falls down in
prostration, the Satan goes into seclusion and weeps and says: Alas,
and in the narration of Abu Kuraib the words are: Woe unto me, the son
of Adam was commanded to prostrate, and he prostrated and Paradise was
entitled to him and I was commanded to prostrate, but I refused and am
doomed to Hell.
حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، وَأَبُو كُرَيْبٍ قَالاَ
حَدَّثَنَا أَبُو مُعَاوِيَةَ، عَنِ الأَعْمَشِ، عَنْ أَبِي صَالِحٍ،
عَنْ أَبِي هُرَيْرَةَ، قَالَ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم
" إِذَا قَرَأَ ابْنُ آدَمَ السَّجْدَةَ فَسَجَدَ اعْتَزَلَ
الشَّيْطَانُ يَبْكِي يَقُولُ يَا وَيْلَهُ - وَفِي رِوَايَةِ أَبِي
كُرَيْبٍ يَا وَيْلِي - أُمِرَ ابْنُ آدَمَ بِالسُّجُودِ فَسَجَدَ فَلَهُ
الْجَنَّةُ وَأُمِرْتُ بِالسُّجُودِ فَأَبَيْتُ فَلِيَ النَّارُ " .
[Sahih Muslim]
Hope that's clarifying and helpful.
